1)if f'(x) exists in some deleted nbd of x₀ in [a,b] and lim x-->x₀⁻≠limx-->x₀⁺ then f(x) cannot be differentiable 2)f:[a,b]-->r be differentiable on [a,b] the

1)If f'(x) exists in some deleted nbd of x₀ in [a,b] and lim x-->x₀⁻≠limx-->x₀⁺ then f(x) cannot be differentiable 2)f:[a,b]-->R be differentiable on [a,b] then the derived function f' cannot have a jump discontinuity on [a,b] What is difference between above statements ?